Consider the following problem.

Maximize Z(

)  (10 

)x1  (12 

)x2  (7  2

)x3, subject to x1  2x2  2x3 30 x1  x2  x3 20 and x1 0, x2 0, x3 0.

I

(a) Use parametric linear programming to find an optimal solution for this problem as a function of

, for 0.

(b) Construct the dual model for this problem. Then find an optimal solution for this dual problem as a function of

, for 0, by the method described in the latter part of Sec. 7.2. Indicate graphically what this algebraic procedure is doing. Compare the basic solutions obtained with the complementary basic solutions obtained in part (a).